of course, i do test. But let's be honest, if the person writing the tests is the same as the one writing the code, chances are the tests won't discover flaws in the model of the original design.

I think there's definitely something to the notion that there will be correlation between things you forget to (try to) guarantee in your code and things you think to test for. It's not clear to me that it's meaningfully stronger than the correlation with things you forget to prove.

Any which way, more prodding of the model (mental or more formal) is probably going to help correctness but may or may not be worth the cost, depending.

Try property testing. Property tests written by myself routinely discover bugs in my codes.

Contrary opinion: Writing your program is much easier once you write the proof, because you basically formulate your entire program.